Posted
by
Hemos
on Monday April 26, 1999 @08:53AM
from the you-got-some-'spalining-to-do dept.

Tal Cohen has taken a close look at Douglas R. Hofstadter's Godel, Escher, Bach -- 20th Anniversary Edition. He's returned to the book to try and explain what the book is really about-using a new foreword. Definitely a book worth checking out - click below to read more.

Twenty years after its original release, the author of this spectacular masterpiece clarifies, once and for all, what the book is actually about.

In an interview to Wired magazine a few years back, Douglas R.
Hofstadter, author of Gödel, Escher, Bach: an Eternal Golden Braid
(GEB for short) complained that most people, even those who actually read
the book, couldn't tell what it's really about. Yes, it talks about music and
art, mathematics and zen, biochemistry and computer languages; but none of these
is what the book is really about.

This seems to be a real problem, because in the new "20th Anniversary
Edition" of the book, Hofstadter says that the question "so what
is this book about?" haunted him since he was scribbling the first
drafts, back in 1973. Now, twenty years after its first publication (in 1979),
the author decided to clarify the matter once and for all, and added a new
23-page preface that, among other things, clarifies the issue.

So -- what is this book about? The New York Times bestsellers
list originally summarized it as "A scientist argues that reality is a
system of interconnected brains".

Hogwash.

The Jargon File (4.1.0) says it's "a brilliant tapestry themed on
the concept of encoded self-reference". Brilliant, yes; but otherwise not
very accurate. Another common definition is "a book that shows how math,
art, and music are really all the same thing at their core". Hofstadter
says he heard this one over and over again, even by people who read the book,
and it is (in his own words) "a million miles off".

My own review of the book (http://www.forum2.org/tal/books/geb.html),
the single most popular page on my web site, says that the book is about
"the question of consciousness and the possibility of artificial
intelligence. It is a book that attempts to discover what 'self' really
means".

Much closer (but I had the advantage of reading that Wired interview).

"In a word," writes Hofstadter in the new preface, "GEB
is a very personal attempt to say how it is that animate beings can come out of
inanimate matter. What is a self, and how can a self come out of stuff that is
as selfless as a stone or a puddle?". His explanation goes on, and
clarifies at least one thing: despite its beautiful playfulness, GEB is a
serious book presenting a serious theory about consciousness. Despite its
popularity, it is not a "popular science" book.

If you already read GEB, you're probably wondering what else is new in
the 20th Anniversary Edition -- other than the new preface. Certainly, there
were many possibilities. Most ideas were about additional chapters -- about
progress made in the last twenty years in the field of artificial intelligence,
or about machine translation, and more. There was also the idea of including a
new dialogue, that was previously published elsewhere. Wilder suggestions went
as far as releasing GEB with a CD-ROM including the Escher's art, Bach's
works and recordings of all of GEB's dialogues by professional narrators.

None of that.

Not a word was changed; not a figure added; not even, the author admits, the
few typos fixed. The book is a facsimile of the original release, with even page
numbering left intact (the preface pages use a separate numbering, from P-1 to
P-23). The CD-ROM suggestion was turned down because Hofstadter "intended
GEB as a book, not as a multimedia circus, and a book it shall
remain". The other suggestions were turned down for more delicate reasons.

But while the preface is the only change, it is a very important one. For
first-time readers, it clears several aspects of the book before they commence
reading. This is important, especially because GEB is anything but an
easy read (some compared reading it to giving birth). For returning readers, the
introduction clarifies many things, and sheds a new light on several aspects.

In addition to establishing, once and for all, a formal definition to what
the book is about, the introduction also describes the history of the book, and
the history of its authors for the last twenty years. You probably heard about
the books he wrote later -- Metamagical Themas, Fluid Concepts and
Creative Analogies, The Mind's I (as a co-editor), and Le Ton beau de Marot: in
Praise of the Music of Language. These books cover much of the suggested
additions to GEB: Fluid Concepts, for example, covers Hofstadter's
research work, while Le Ton beau de Marot includes a lengthy discussion
(or rather, a lengthy attack) on machine translation -- among many other things.

The preface also talks about GEB's translations, a suggested
sex-change operation for the Tortoise, a brief account of Hofstadter's recent
literary efforts, and more.

Since you probably owe yourself a re-read of the book (you did read it
before, right?), the new edition is a good excuse as any to start now.

The book was a hype a generation ago, and it is one of those things that makes me feel old because I can't share my thoughts with younger people who've never heard of it. Yet I remember the disappointment when finishing the book: all through the book he works to prove Goedels theorem (that was what I thought the book was about). In the end Hofstadter does some flumsy handwaiving, leaving me completely unconvinced of Goedels theorem and its implications. I then sought and found a convincing explanation of the theorem in a booklet by two Dutch logicians, much thinner than GEB, but so much more boring to read.

I believe a problem with GEB is that it propagates the view that Goedel's incompleteness theorem is about self-reference. It took me years after reading GEB to realise that the theorem is actually about ambiguity.

The way I understand it today : suppose you wanted to formalize a dictionary - to make the definitions of a dictionary mechanically constraining. What the theorem says, is that this will not make ambiguity disappear : your whole dictionary will become ambiguous. At some point, it becomes possible to redefine many terms of the dictionary simultaneously, in such a manner that their definitions don't change. The "new" meaning of a term is given by reading the definition, using the "new" meaning of the words forming the definition, while the "old" meaning is obtained by reading the very same words according to their (respective) "old" meaning.

Further, such "symmetries" are function of the current state of the (incomplete) dictionary, which means that, while a single state of the dictionary covers many consistent interpretations of it, the correct wording for the definition of a new entry, may *not* be indifferent to the interpretation you choose for the dictionary (as it is before adding that entry).

Now GEB possibly states something very much like this, I don't remember : but the fact is that it insists so much on the self-reference in Goedel's proof that a view such as the above one appears at odds with what GEB says.

Yes, this is in the bibliography. Also, Achilles and the Tortoise mention it a few times--- supposedly, a friend of one of them is writing it.

Anyway, here goes. On page 748, at the bottom:

Gebstadter, Egbert B.

Copper, Silver, Gold: an Indestructible Metallic Alloy. Perth: Acidic Books, 1979. A formidable hodge-podge, turgid and confused--- yet remarkably similar to the present work. Professor Gebstadter's Shandean digressions include some excellent examples of indirect self-reference. Of particular interest is a reference in its well-annotated bibliography to an isomorphic, but imaginary, book.

I admit that when I first tried to read it I didn't understand whole chapters. I did like the conversations though....and yes, I changed my major and wrote a college honors thesis based on his framework and his bibliography. His metamagical themas is less technical and for me...much more accessible as a non quant.

Don't bother with multi media...just seeek out all the sources yourself.

It is an excellent book... I read it just to look intelligent, and didn't understand a shitload (read it in 11th grade) but the stuff I DID get blew me away (I particularly liked the conversations between Achilles and the Tortoise... like the phonograph...)

I recently Produced and Directed a play based on GEB, called "Prelude, Ant Fugue". It included two Acts and the scenes were Three Part Invention, Solo for unaccompanied Achilles, Crab Canon and Prelude, Ant Fugue. When I asked Prof. Hofstadter even he tried to convince me that P,AF was too hard to present on stage! lol.

I guess all this makes me a fan:-)

I even have Escher prints up in my house. After all he is my favourite artist. In any case, I've got a print of Mosaic II hanging on my wall, in plain view from here:-)

Maybe I should read it again. I tried 20 years ago and I thought it an oversized self-indulgent book - like a pompous academic talking to himself. I gave up after 100 pages because I didn't see the point.

But so many others here like it, so like I said, maybe I should try again.

In reading all your comments, the answer occured to me why today Bach is my favourite compositor and Escher my favourite artist (along with Kandinsky). The answer is: I first read GEB aged 16, too. Back then, I didn't get all of what it said, especially the Gödel part, today it's one of the books I enjoy reading again and again now and then. (And I still don't get everything.)

This is a book which, as is hinted strongly in the RICERCAR, you get more out of each time you read it. I haven't read it in 4 or 5 years, so I should probably read it a few more times, but I used to make it a point to read it every year or so.

Think of this as a philosophy text from a mathematician. Some people will see it a gibberish, some will see only the specifics of the text, others will have their thinking jolted by the book. The final group is the one that doesn't "know what it's really about". Every philospher and philosophy professor should be required to read this book once a year. It would do a great job on the "skullful of mush" problem.

I started reading GEB:EGB back freshman year in college, and I still go through parts of it just because it is fun. I disagree with some parts of it, but I don't think that makes it necessarily *bad*.

One think I liked about it: he'd be talking about music or biochemistry or logic, but his point would be from some completely different area. He'd sneak in little things, even small things like the tortose saying "Tata". Pretty cool.

Of course, it's nonlinear nature is something I liked. Some people don't like that kind of thing.

Its not like other books where words form sentences, which more often than not make sense right away. In GEB you have to put forward a little more effort to understand whats being read (ie, think). And because I can feel how much it is enriching me, I stick with - progress is slow; but steady.

If you were really interested in a superconcise, plain-English statement of the theorem, you'd look up Kurt Goedel in the Columbia Encyclopedia.

While you're probably right about people getting the wrong idea about the _end_ of Goedel's theorem from GEB, GEB is really more about illustrating the _process_ of Goedel's theorem. (Draw up this funky-looking theorem that proves theorems, load the theorem into itself, and what do you get?)

You get a better idea of what a car's purpose is from watching a Mercedes commercial than from watching a mechanic poke around the engine, but sometimes watching the mechanic is better if you want to see how it works.

I've read this book too many times to count. It's in pieces because of my abuse. I hate math with a passion, but this book made things clear to me (just like "The Discoverers" did for history).

I am a lender of my books, especially ones that I love. However, this book has never been leant out. My girlfriend had to wait until we moved in together to be able to read it. It is too precious to me to let it get out of my apartment.

Well, now I will buy a new copy, and the old will be taped up and lent out. I can't wait to have a freshly bound copy in my possession. I will try to make this one last a little longer.

The first time I knew about the book was from an article from the Whole Earth Review (WER)... and then the same book was mentioned in one of the computing/technology mag, and that got my interest.

So, poor student like me who couldn't find enough money for tuition fees (by skimping on FOOD !!) generally chose to "borrow" the book from the library (hehehehe, still have it with me, hehehehehehe) and for once, I DO NOT REGRET I STOLE THE BOOK BECAUSE THE BOOK WAS CERTAINLY GOOD ENOUGH FOR ME TO STEAL !!!!!

The above, folks, is _my_ review of the book.

Am I thinking of stealing the NEW version of the book? You bet I am. Hehehehehehe

And partly because I despise math with a hatred unseen by mortal eyes. It's much too impersonal to me, all absolutes and nothing much of beauty in it. I know enough math to get through life and that's all I feel I need. But, back to the book.

Okay, now although I'm like most people who have posted and loved GEB (I read it just before I got out of the service to goto college...before I read it I was going to study ME, basically the design end of my Navy job...read it and changed majors before I even got to school...) I understand not everyone does like it. I will even admit I think some people who love it do so just because they are afraid to admit they were confused (hell, I'm lucky if I got 10% of some parts).

I cannot however let Mathematics be insulted without punishing the transgressor (: Seriously aphr(), there is much beauty in mathematics. If you are willing to give mathematics a second (third/fourth/fifth/whatever) chance, I would recommend a good intro text on group theory (I would recommend Contemporary Abstract Algebra by Gallian, probably could find a used one at a local university). Group theory is, among other things, about symmetry and can be found in Escher's drawings as well as crystals and quantum theory. I cannot think of many things more beautiful than a construct of the human mind that captures symmetry (a personal aesthetic favorite anyway).

I read this book a couple of years ago and excuse my ignorant heathen-ness, but I didn't like it. Partly because, like he says, I didn't know what the hell it was supposed to be about. And partly because I despise math with a hatred unseen by mortal eyes. It's much too impersonal to me, all absolutes and nothing much of beauty in it. I know enough math to get through life and that's all I feel I need. But, back to the book. Overall, I didn't enjoy it mostly because of the constant references to mathematics.

Perhaps I'm the only one who was either too ignorant to get it or the only one who's not trying to sound intellectual by saying I got it. Who knows.

P.S. - If you find The Mind's I, by Douglas Hofstadter and Daniel Dennett, GET IT. It's a wonderful book. Greatly entertaining book, especially for the philosophy genre.

Read what I said... It's much too impersonal *to me*, all absolutes and nothing much of beauty in it...

To ME. I do read lots of philosophy, mostly dealing with ethics and morality, however, not AI or mathematics. I carefully stated my opinion that way because I know that beauty is in the eye of the beholder. Before you say anything, yes I have tried out mathematics; I've toyed with it and just didn't find it interesting or worth delving into more.

The reason I got the book is because I heard everyone raving over how great it was and I could become impotent of I didn't read it, etc.

I have to say I had the opposite impression. GEB bored me after a while - it all seemed trite, simplistic and obvious and I never finished it. Penrose's books (Shadows of the Mind is the followup) OTOH seemed to proceed from the assumption that we don't know it all and suggest where we might go looking (even his opponents have praise for the review of physics in ENM). There are many interesting questions relating to minds that physics doesn't even know where to begin (one that Penrose doesn't even mention is: Why is there a present moment - not just past and future).

One of the most interesting non-traditional QM theories I have seen is the transactional interpretation put forth by a UW professor. Read all about it. [washington.edu] I personally think that what makes us _not_ Turing machines is our ability to comprehend infinity on some level. Strong AI claims that this is an illusion, but TI provides a mechanism that allows for infinite computations in finite time which means that it might not be an illusion after all.

As marks against Penrose, I completely understand the problems with his arguments, but his strong AI opponents have not proved their own case either. Given a choice of where to proceed I come down on the side of present ignorance. History has too often shown that just when we think we know it all something is about to whack us right between the eyes.

Yes! AI is plauged by the old "If all you have is a hammer then everything looks like a nail" problem. Or in their case, "If all you have is a Turing Machine then everything looks like an Algorithm." This can be very productive (cf. Khun, The Structure of Scientific Revolutions) and I think that the stuff AI has come up with plays some part in the Big Picture, but paradigms are also limiting and a certain degree of humility is appropriate.

Incidentally, another good layman's book on the embodied mind is Antonio Damasio's Descartes' Error: Emotion, Reason and the Human Brain

I hear ya- been a few years since I started, with no end in sight. It's a hard slog at one level, but some of the ideas are beautiful, and I find them popping into my head at odd moments. Maybe the problem is that reading it is a bit too much like studying- without an exam you know you won't finish! Maybe when I'm finished studying it will be easier to read, because I will need the challenge. Now I need to read to escape the hard stuff I'm studying. (Pratchett, anyone?)

Can it really be 20 years since GEB came out? It doesn't seem possible. I guess it had been out for three or four years when I discovered it on the shelves of my university bookstore. I had never heard of Douglas Hofstadter, but I knew about Bach and Escher, and Martin Gardner's words printed on the back cover were the clincher. Every few years since then, I get out GEB again and re-read -- sometimes cover-to-cover, sometimes just the fun parts. It never fails to entertain and enthrall.

BTW, speaking of AI... a coworker here -- PhD, AI expert, former NASA flight controller, and hacker -- has told me that Alice in Wonderland is one of the best AI books ever. Don't know whether he was talking about just Alice's Adventures or both that and Through the Looking Glass, but I intend to go re-read both to see what he was talking about.

I've had this book for about 10 years now, and have read it all the way through three times, and have referenced it many more.

When I first got the book, it was because of my interest in AI, and I thought the book would be just about that. I was surprised (and pleased) that it turned out to be *much* more. The dialogs, especially, did a great deal to clarify the more technical tone of the chapters, and were extremely entertaining, as well.

From his insightful treatment of number theory, including the best discussion of Godel's number (and what it means) that I have ever encountered, to wonderful examples of self-reference and symbols, this book has gained a permanent spot in my library, and I would recommend it to *anyone*, even the non-technical among us.

Also, as a musician myself, I was pleased by the extent that music played a part in his arguments, especially since Bach is one of my favorites.

To me, this book represents the definitive examination of intelligence, and especially self-awareness from the symbols and mechanical systems that underlie them.

I actually did finish GEB, years ago. It's Fluid Concepts and Creative Analogies and Le Ton Beau De Marot that i can't finish. I haven't finished Minsky's Society of Mind or Pinker's How The Mind Works either.

I simply haven't finished them yet. (Ever hear of the Halting Problem? *grin*)

I've always found that the best books force you to read them in small doses, then you have to put them down for a while to digest their implications. All the books I mentioned before are like that for me. Sometimes the implications are emotional rather than intellectual, suce as in the case of the Ethical Slut.

I've been reading this book for over six months (i do a lot of work, so i don't have oodles of time to soak up the immensity of the task and it's not exactly just-before-bed reading material). And all the while friends ask me what it's about--and why it's taking me so long to read (i usually read stuff pretty fast--one three-day weekend i read 5 vonnegut books (the scars have healed--thanks!)).

I'm glad I'm reading it just after college as it is connecting many many many things I've read, experienced, and felt during my college extravaganza. It is truly a marvel of a book.

But I disagree with the attempts to summarize the book. All summaries of the book (and I'm not being cheesy, and I'm not trying to be cute either--I really think that this is the best and most complete answer given the set of all combinations of human vocabulary) should be as follows:

I may say this book is the best I ever read ( and I've read a lot along my life ). I think GEB is about lots of things. About multiplicity of levels of reality, about what self-conciousness ( what's that and how that can be achieved from unconciouss matter ), about AI. The book is also about beautifulness in mathematic, music and pictorial art. I'm sure most people that would never read it, are missing a lot ( because it could teach THOSE people to appreciate the mistery hidden in the universe, but this lack of appreciation is the reason they won't read it ). And finally, is clearly a book to enjoy. Every word, every page. Very clever. Difficult, may be, but surely worth the effort.

This book is quite possibly the *best* book I have ever read. Not only is he an entertaining author, but some of the content inside is profound enough to leave a lasting impression on you for the rest of your life, and, quite possibly, teach you something.

If you haven't read this book yet, I urge you to go out and find a copy. Amazon and Chapters seemed to have trouble stocking the old version, but it should be out there somewhere.

When I was in college, I used to incorporate technical subjects in my papers for non-technical classes because I knew the professor, being unfamiliar with the subject, would have less opportunity for criticism. It worked pretty consistently. I think the same is true with most of Hofstadter's audience, especially those who awarded him a Pulitzer Prize.

Clarity and efficiency are the essence of good writing, and GEB has neither. It's a 700 page stream-of-consciousness rambling, with very little focus or organization. Doesn't it strike anyone as odd that it took him 20 years to figure out what the book's about? Hofstadter is a smart guy and he has some interesting things to say, but in my opinion he's a pretty lousy writer.

Furthermore, being intelligent doesn't necessarily mean you are knowledgable. I can't say much about Escher or Bach, but Hofstadter's discussion of mathematics, biology, and computer science is pretty amateur. Although the subject matter he discusses is indeed profound, it's nowhere near as mystical or difficult to understand as he makes it out to be. The best things in GEB are citations and retellings of work by greater men than Douglas Hofstadter.

Smart people frequently make the assumption that intelligence equals knowledge, and that just because they are knowledgable in one area, they can speak authoritatively about all things. Standards are pretty low in world full of mediocre people, and it's an easy mistake to make.

P.S. Another example of a good book that's about 5 times as long as it needed to be is "Atlas Shrugged".:-)

Because a friend told me about the book, I searched Columbus bookstores until I found the paperback 20th anniversary ed. It's great. As bedtime reading, I can't think of anything better. It leaves your brain drenched in new thoughts and ideas (and makes for interesting dreams). Continuing to streach your mind out of school can be difficult at times. It seems you get stuck in a rut and can't find a mental challenge anywhere. That's where I was when I found this book. Hofstader's book made me rethink the way I look at things, and remember the simple complexities of life.

Oh, you are soooo wrong. Try it out... you'll find out why no one can tell you what its about. It's about nothing and everything, logic/music/art/computers/intelligence, and yet its not about these things, but merely uses things to explain itself. It's about self-reference, and yet it is self-reference.

I got to read some of this book in my logic class. Being a philosophy major with a music background, I found this book both informative and exciting. The short stories with Achillies were great, as was all of the writing. It takes a skilled hand to take bone dry musical/numerical theory and transform it into interesting practical stories. I'd recommend it just for the fun stories--especially if you like theory (musical or otherwise).

When I was in college, I used to incorporate technical subjects in my papers for non-technical classes because I knew the professor, being unfamiliar with the subject, would have less opportunity for criticism. It worked pretty consistently. I think the same is true with most of Hofstadter's audience, especially those who awarded him a Pulitzer Prize.

I see your point. GEB is a book that you should like, just like the the emperors new clothes. Its a highly enjoyable book to read though, and your statement: Clarity and efficiency are the essence of good writing, and GEB has neither. sounds a bit too harsh to me. When I read it (as a teenager) I loved it, but I certainly did not understand all of it. It is certainly not a good way of presenting a theory, but as amusement it is great!

That Hofstadter now explains what the book is about is IMO to spoil things. Its like the case with the Koans in the book, once a koan is explained it just becomes a boring statement. A statement that, in this case even is based on outdated premises (see other postings here about the AI fallacy). The riddle is the essence of the story, because then you are not limited by the imagination of the author, but can fill the gaps with your own imagination. Same reason why people like X-Files I believe;)

The best things in GEB are citations and retellings of work by greater men than Douglas Hofstadter.True, but this does not necessarily belittle GEB as literature. Often the original sources are less interesting to read, and reading GEB would be a good way to get interested in these ideas.

P.S. Another example of a good book that's about 5 times as long as it needed to be is "Atlas Shrugged".:-) And just like GEB it is based on weird assumptions--objectivism doesn't hold any more than traditional AI;)

In fact, I'll be more specific. For a guy who has been fascinated with that particular philosophical question (how "self" can come out of the goo of everyday matter) since high school... this book was, quite literally, life changing. And, ironically, I don't even feel that my grasp of the concepts in the book are as good as they should be.

I discovered DRH's books quite by serendipity. In March 1986, I was on spring break in high school, and tragedy struck: my C64's power supply was fried. I was such a damn nerd that, since my computer was dead, I couldn't think of anything better to do than go to the library and read about AI.

I remember browsing around though various AI books, looking for something interesting, and then I somehow drifted into the Math books. I misread the title of one of the books. I *thought* it said "Mathmatical Themes" but I wasn't paying a lot of attention, I guess, so I picked it up.

I opened it to a random spot, and there was a LISP program. "Oh, I must have drifted back into the AI books," I thought. Then I turned to another page. There was an aerial picture of a bunch of logs in a river, and a caption that talked about guessing how many logs that was. I was confused. Was this a math book or an AI book? Then I turned to another picture with a bunch of boxes and dots, and it was comparing the worldwide nuclear arsenal to the total firepower of WWII. Then, in frustration, I looked at the title again and saw my error. It was called "Metamagical Themas." I probably wouldn't have given the book a second look if I had correctly read the title earlier, because I was far too geeky to read "new age" stuff about "magic" and the word "themas" conjured up images of sissy "literature" stuff. Hey, I was 17 and that's just the attitude I had at the time.:-)

Anyway, the book entertained me for the next few weeks. The best part was that it referenced other books that turned out to be even more fascinating, like Hofstadter's "GEB" and Richard Dawkin's "The Selfish Gene." GEB and TSG turned out to be some of the most interesting and stimulating books I've read in all my life. And it was all due to an accidently misread title!

My personal GEB experience: When I was finally forced to accept a degree, after ten years of studious avoidance, the degree I accepted was of the English Lit variety, as opposed to something really useful like CS or Mathematics. However, ten years at the academy did allow me to drink with members of a wide variety of Disciplines; I did in fact read most of GEB and chatted about it ad nauseum. After that bit of extended research I can testify that it is just as likely that a student of CS, AI, math, etc, has read GEB as it is likely that an English Lit student has successfully read James Joyce, and for exactly the same reasons and with similar levels of deliberate obfuscation.

many people are claiming to be enamored by this book. what do these people think of mathematics? my experience has been that not very many will admit to liking the subject with any degree of enthusiasm -- especially computer scientists. (and forget the question "how much do you know of it?").

well, anyway, i claim that this book is essentially a math book. it is padded, but it's a math book. and i have a bone to pick with the secondary education system for convincing people that because they can't factor polynomials quickly, they won't enjoy what math _really_ is. (the cause? high school math teachers don't know math).

oh, and anyone that says this is not a popular book ought to read "uber formal unentscheidbare shatze der principia mathematica und verwandter systeme" and tell me what they think of that.

concisely, godel's first incompleteness theorem says that in arithmetic (or any system that contains arithmetic), there are statements that cannot be proven nor disproven. (arithmetic is 0, 1,... with addition and multiplication).

godel's second incompleteness thereom states that the consistency of a system cannot be proven within that system (a consistent system is one in which it is not possible to prove both a statement and its negation).

Many years ago I read a science fiction short story about a team of guys performing research into AI and maths and logic etc. Now the author took the premise that the human mind was some kind of computer, so when these guys finally reached the "ultimate thought" in the course of their reasearch it "crashed" their minds. They just stopped and eventually died. When the reaserch database was moved over to a new facility and another group took over the work they to began to "crash" and die as they too found this ultimate thought.

Well I read GEB in 1984 and I think it almost crashed my mind. I havn't been able to think in straightforward, decidable, non-recursive, complete way about even the simplest things ever since.

WARNING - DO NOT READ THIS BOOK, YOU MAY NEVER RECOVER.

Anyway somehow I think I have to get myself a new copy and go around the loop a few more times:)

P.S. Does anyone have a an idea of the author/title of the story above ?

I would very much like GEB in cd form. I often turn back to look something up in it. It would be especially nice if they included the music. Too bad they won't. It is a real loss. Not to mention that a cd might make it more accessible to disabled users.

I haven't finished life, either, but I'm not about to say that I don't think it's good.

GEB:EGB was not simply a collection of facts to be absorbed, like a text book. It is a stream of consciousness, to be experienced. reading it enriched my life. I was disappointed when i had finished the book, as a pleasant experience had ended. Reading the book again was not as enjoyable as reading it for the first time; the information was the same, but I'd already experienced it.

GEB is a marvelous and wonderful book and every moment working through it is well spent. and it is work.

A key notion that undergirds the book is that of Strong AI. to wit, the notion that every mind you ever encounter is purely software running on some sort of computational hardware: be it a neural net or a termite hill or a massively computer.

I suggest that a good counter-point to GEB is Roger Penrose' _The Emperor's New Mind_ that suggests that the mind emerges from some kinda quantum process within the neurons.

Penrose notes that if Strong AI is correct, then each mind can be implemented on a Turing machine. this gives the mind an ontological status similar to that of the theorem of pythagorus or the quicksort algorithm. This is a delightfully ironic platonic consequence of a decidedly non-platonic start-point.

Absolutely! I believe that (16) was about the age I was when I read it too. It was, IIRC, a Birthday present; I'd requested it because I liked Bach and worshipped Escher. 2 out of 3 ain't bad, right? I'd never even heard of Godel. I had NO CLUE!

To say this book overpowered my poor unprepared teenage mind would be a serious understatement. I loved it!

A quote from the come-on text on the back of Neal Stephenson's The Diamond Age (since you mentioned it) could apply equally well to GEB:

"People who plow through these mind-bogglers will walk around slack-jawed for days and reemerge with a radically redefined sense of reality"

Well, I bought one of the early editions, 15? years ago. I've read every word in it, several times, but can't say I'm finished reading it yet. I may have to buy a copy of this edition, mine is looking a bit tattered. ***********************************

"Alice In Wonderland" (both books) is one of the best introductory texts on any subject whatsoever. As for GEB, I have to admit I've had a copy for several years and still haven't made a very sizeable dent in it. But I *have* read and enjoyed "Metamagical Themas", which may be a better point of introduction for the Hofstaeder newbie -- it's a collection of columns from Scientific American, and covers much of the same conceptual ground as GEB, in a more approachable bite-sized format (that does *not* imply anything is glossed over or dumbed down). I also highly recommend "Fluid Concepts...", edited by Hofstaeder, which is an *excellent* book on AI theory and concepts -- it gave me lots of great insight as to how pattern recognition systems are designed, using lots of interesting examples ranging from the extrapolation of mathematical sequences to linguistics to cryptography.

I read this book when I was sixteen, and it is undoubtedly the profoundest literary influence on my life since then. All of my interests in automata, machine intelligence, formal logic, and mathematical computing can be traced back to reading this book all those years ago.

In all honesty, I think I probably would still have ended up as a programmer without reading this book, but I wouldn't be the same person and I would have less of a sense of wonder about it all.

As it happens, I'm in the middle of rereading Neal Stephenson's The Diamond Age - I reckon GEB is A Nerd's Illustrated Primer.

Nice observation maggie -- there is yet another level of self-reference embedded in geb(egb). That is, there can be no algorithm for determining whether a given Turing Machine (or wetware) will halt when operating on a given input (or book).

This is not incompatible (i.e. it fails to avoid being not incompatible) with our valuable grey stuff being Turing-equivalent. Un/fortunately it is not a proof.

Actually, the way I read geb (in my teens) was a bit like a TM, shuttling backwards and forwards, with each transition altering my internal state. I did get to the end then. I wonder if my thirtysomething TM program will halt?

Excuse my ignorance of the book (having not read it myself), but how good can it be if absolutely noone knows what it's really about? Sounds like a lot of people are jumping on the bandwagon to say how good the book is just to look intelligent.

Well the first chapter was very good. After that he seemed to be spending a whole book saying the same thing he said in the first chapter. After a while I started highlighting things which I perceived as logic errors. Finally it wasn't worth my time any more.

Anyway, thanks for telling me the ending. Now I can be satisfied that I didn't miss out on anything.

I read it and I have no idea what it's about. For me, it was like reading an object-oriented design textbook : endless demonstrations of abstract and useless ideas. I kept thinking "would you just get to the point?".

I've owned several copies of this book since I first read it in the 80s... all of them lent out and never returned. This looks like a good opportunity to add it to my bookshelf again (as a shiny new one, and not a ragged second-hander like most of the other copies I've had).

To those who haven't read it, I can't recommend it highly enough. Yes it's a hard (or at least long) read, but is it EVER worth it! This thing is a complete masterpiece, in places an absolutely dizzying display of inspiration and genius.

I'd have to disagree. I was hoping for a good counterpoint but I felt that ENM was by far inferior to GEB. Obviously the subject they tackle is very involved and both spend a good deal of time setting up the intuitions however I found that most of ENM was irrelevant to the main point (or at least the connection was not made clear at all.) The conclusion I got from ENM was that if Penrose's oddball (by his own admission) quantum theory is correct than there is a faint possibility that the strong AI conjecture is false. Its an awful lot of book for such a weak argument.

The one point in ENM's favour is that it is the first argument I've seen against strong AI which is not directly based on circular definitions (ie definitions of intelligence which include the requirement that the subject must be human, amongst other things.) Unfortunately I don't think the case was made well.

It was to me anyway. I read it aged 16 and understood maybe 2% of it (if that). But I can look back and say it sparked my interest in programming, classical music, Escher and mathematics - all of which I retain at age 32. Nowdays each yearly read yields maybe 1% more understanding:)

I read the book. I found it entertaining. Beyond that, I wouldn't say it was worthwhile. After all, it goes on for 800 masturbatory pages to reach the completely generic conclusion that AI is possible.

A lot of people seem to be so taken with this book. I can only conclude that the enormous satisfaction of solving the little puzzles and games sprinkled through the text outweighs the enormous letdown of the text's message.

If all you got out of it was the stuff on AI, then you really weren't reading it very closely...:) IMHO, GEB really isn't a book for everyone. If you're a conclusion/goal oriented person, then GEB is NOT for you. There is no earth shattering conclusion. GEB is a book for people who believe that the journey is more important than the goal, that all the little tangents really are important, and the thoughts that are inspired by a book are just as important as the thoughts that get spoon fed to you.

Perhaps you mean _Consciousness Explained_. Anyway, I don't think that believing in the possibility of AI indicates a lack of understanding of the current debate. Perhaps what was wanted was a more substantive picture of HOW AI might be possible. I haven't read the book, and i'm just going from the content of the comments in this thread, but personally, if I read an 800 page book whose conclusion was AI is possible, I too would be disappointed. If Hofstader did more than that, good for him. If he didn't, then I would suspect the book is indeed 'masturbatory'.

And I think it would be worthwhile to avoid the Dennett in any case. He's a skilfull metaphor crafter, but not philosophically very deep.

I read GEB when I was an undergrad in CS. (That wasn't really 20 years ago, was it?!?) I was just barely able to follow the math and AI theory. But thanks to the Escher and Bach interludes, I got a chance to stop climbing mental mountains and enjoy the scenery.

In the new preface, DH says, "GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter." (I will be rereading it with that in mind.) This is more than just AI. For some additional insight into this theme, check out "Emergence: From Chaos to Order" by John H. Holland. I think he even references GEB there.

Hofstadter is so bloody intelligent that it's easy to be blown away by it and just say, "Oh, Mr. Hofstadter, you're so right, I had NEVER noticed that! I think I'll sit around and make recursive acronyms and ambigrams now!" Pshaw.

Hofstadter's a lot better than many AI researchers on this score, but he *STILL* underestimates the degree to which bodies are bound up together with minds. His insistence that perception is bound up with cognition is a step in the right direction but he still falls into the old "mind is software and portable; body is hardware and dispensible" schtick that has plagued AI research since its inception -- in short, the tendency to literalize the "mind as computer" metaphor.

Read him and try to follow everything he is saying and then don't just sit back and accept; *argue* with him; read, for example, the work of George Lakoff, Mark Turner, and Mark Johnson on the embodiment of the mind, or Gilles Fauconnier on analogies and mental spaces, to get some further, less intricately and elegantly expressed, but in some ways more important perspectives on these issues.

To be specific, read GEB and then pick up George Lakoff's _Women, Fire, and Dangerous Things_ for a less hip but equally mind-expanding trip through cognitive science.

Even if you don't finish this book, it is bound to upset you. It resonates on a lot of levels and gets on your nerves in a positive sense. Even if you disagree wholly with its message (which is easy to do) it provokes you to think and talk about it. I think that is a hallmark of a great book (although I would refrain from calling it literature, as some folks do). In this respect it always reminds me of Pirsig's "Zen & the Art of Motor Cycle Maintenance". --

I was just coming into my own mathematically speaking when GEB was published. At the time, my comprehension of Godel's work was then still just at the level of Nagel and Newman (which is a better exegesis of the theorem itself). The few philosophical pieces on Godel's work were at the time incomprehensible to me, and most of the pop science stuff was even then transparently implausible.

Then, Douglas wrote his book.

Now, at the outset, let me say that I agree with almost all of the criticisms, including the allegations of self-indulgence and pretensiousness.

But so what? GEB *IS* a beautiful book, beautifully published. It is thought provoking without being intellectually nihilistic (as many paradox-mongering pieces are -- you know what I mean, the vacant-eyed "wow, what a concept" pieces).

So what if many people finish the book thinking they understand Godel when they have missed the point -- and probably never will get the real meat out of it formally? So what if it is too often wielded by the ignorant as authority for the "fact" that Godel means [fill-in-the-blank]?

GEB was FUN!

Here, since we're all nerds -- try this: Express using only predicate calculus the proposition "x is a power of 2."

This was just a throwaway in the book, but it was actually a few years before I found an elegant solution, and when I did, I truly felt that I had "gotten it," at last, why the calculus is so powerful and why algebraic expressions would obviously admit self-reference. A three-star problem that was truly worth the journey.

Go ahead.

Then look at Scott Kim's pictures again.

Then read the lovely dialogues.

Then spend a few years studying --and I mean really studying Godel's theorem, metamathematics and the underlying philosophical works addressing the same-- study so that at last you are able to articulately criticize the book effectively for its failings and informalities. Write the essay, and then you will realize that you, too, have missed the point.

Later in life, I wanted to explain to lawyers why some jurisprude's hopes of a purely formal legal system were not realistic, so I wrote a piece, desperately trying to "dumb it down" enough to be comprehensible, while keeping it real enough to be mathematically defensible. You have no idea how hard that is until you really try to do it. (If you are inclined to see how amateurs do it, check out Brown & Greenberg, On Formally Undecidable Propositions of Law: Legal Indeterminacy and the Implications of Metamathematics, 43 Hastings L.J. 1439 (1992)).

While I believe I now understand, at last, Godel's theorems well and deeply, not so much because of GEB, I now understand for certain that the heart and passion of those great works of an early twentieth century mathematician do seem to lie, at the end of the day, in the very playfulness of the subjects of Professor H's book.

He didn't fairly capture the essence of the mathematics, but he did capture its heart and soul. He didn't teach me what I needed to learn about the theorem, but he did teach me how and why I would love it once I did.

And for that, I am still much indebted to Professor H. The book is clearly flawed, yes, but it still took my breath away.

And THAT, IMHO, is why this book won a pulitzer. As a math textbook, this book is very deeply flawed in many ways. But as a piece of non-fiction, GEB is a bright, shining jewel; particularly when viewed in light of the vapid "Hey, man, what a concept" paradox-mongering alternatives.

Godel's original paper is actually quite readable to anyone with even a basic mathematical background. I took a course on mathematical logic last spring, and the prof just had us all read the paper itself rather than using any text. You can probably pick up a copy at your local university library. It's well worth the read if you're having trouble understanding what his theorem is all about.

Oh, wow. Reading "Godel, Escher, Bach" was an almost religious experience for me. Yes, it took a while to get through it, but that book made me start classifying myself as a wanna-be cognitive scientist.

Very seldom in one's life do such experiences occur.

"Metamagical Themas" is also a good read, and more general (lacking GEB's linking themes of self-reference and cognition). "Le Ton Beau de Marot" has a lot of interesting things to say about machine translation, but Hofstadter also says some rather silly things about linguistics.

If you're even slightly interested in cognition or AI, you should go out and read GEB if you haven't already.

What sort of thing do you want to hear? The problem is that different people get different insights out of GEB; this fact does not invalidate those insights.

At one level, all the book says is that intelligence is possible. At another, it discusses some of the parallels in music, art and mathematics. At another, it's about brains; it's also about number theory, Zen, and the genetic code; it's about self-reference and analogy, and it's even a parody of (or homage to) Lewis Carroll.

The parable of the five blind men and the elephant doesn't disprove the existence of elephants.

The point is that no one knows what *the author thinks* it's about. It means different things to each reader. I found it a fabulous cross-discipline primer in structured thought when I first read it at 17. I didn't take out if it the same theological or metaphysical concepts that others found.

In later readings, I have focused on other aspects of the book. No matter how you read or interpret it, GEB is a fabulous read, and will stimulate your thinking.

The reason many people have so much trouble saying what GEB is "really" about is that on fine scales it's about a lot of different things: math, music, Zen, wordplay, AI, and so on. However, there is a unifying theme behind all of these topics. In this respect the book is similar to the Bognard problems (BPs)of Chapter XIX. In each BP each panel is about something different, but the real subject isn't spelled out explicitly; it has to be deduced from the "microsubjects."

I don't think it's quite correct to say that "absolutely nobody" can say what GEB is about. It really isn't that hard to figure out, but it does require the reader to think about it a bit. This book is by no means a light read. In this respect it is no different than any other substantial piece of literature (or art, or music, or mathematics, for that matter). Still, if you are willing to put forth the effort, you will be well rewarded. Give yourself a treat: read this book.

Next week: all about the time I was riding my bike around campus and nearly ran over Douglas Hofstadter -- my brush with fame!